Montgomery algorithms represent a transformative advancement in the computation of modular arithmetic, specifically designed to bypass the costly division steps inherent in traditional methods. By ...

High-performance matrix multiplication remains a cornerstone of numerical computing, underpinning a wide array of applications from scientific simulations to machine learning. Researchers continually ...

Want smarter insights in your inbox? Sign up for our weekly newsletters to get only what matters to enterprise AI, data, and security leaders. Subscribe Now Can artificial intelligence (AI) create its ...

Mathematicians love a good puzzle. Even something as abstract as multiplying matrices (two-dimensional tables of numbers) can feel like a game when you try to find the most efficient way to do it.

We study probabilistic extensions of classical deterministic measures of algebraic complexity of a tensor, such as the rank and the border rank. These probabilistic extensions enable improvements over ...

With AlphaTensor, DeepMind Technologies has presented an AI system that is supposed to independently find novel, efficient and provably correct algorithms for complex mathematical tasks. AlphaTensor ...

What do encrypted messages, recognizing speech commands and running simulations to predict the weather have in common? They all rely on matrix multiplication for accurate calculations. DeepMind, an ...

This summer, battle lines were drawn over a simple math problem: 8 ÷ 2(2 + 2) = ? If you divide 8 by 2 first, you get 16, but if you multiply 2 by (2 + 2) first, you get 1. So, which answer is right?

In 1971, German mathematicians Schönhage and Strassen predicted a faster algorithm for multiplying large numbers, but it remained unproven for decades. Mathematicians from Australia and France have ...

David Harvey receives funding from the Australian Research Council. Around 1956, the famous Soviet mathematician Andrey Kolmogorov conjectured that this is the best possible way to multiply two ...